Euler's Method/Improved Euler's Method
显示 更早的评论
Having trouble working out the bugs in my Improved Euler's Method code. I previously had trouble with the normal Euler's method code, but I figured it out.
Euler's Method (working code):
syms t y
h=0.01;
N=200;
y(1)=1;
t(1)=0;
for n=1:N
k1=1-t(n)+4*y(n);
y(n+1)=y(n)+h*k1;
t(n+1)=t(n)+h;
end
plot(t,y)
And here is my attempt at Improved Euler's Method:
h=0.01;
N=200;
y(1)=1;
t(1)=0;
for n=1:N
k1=1-t(n)+4*y(n);
k2=1-t(n+1)+4*(y(n)+h*k1);
y(n+1)=y(n)+(h/2)*(k1+k2);
t(n+1)=t(n)+h;
end
plot(t,y)
The error message that pops up is "Index exceeds the number of array elements (1)." I'm rather new at MATLAB, and don't know what this means, can someone help me rework this? Thank you!
2 个评论
Lucas Howarth
2020-10-9
Mike Asmanis
2021-6-18
Hey , how would i be able to solve this : y'(t)=cos(t + y) y(0)=0 t[0,3] exact solution y(t)=-t + 2arctan(t)
using your code?
采纳的回答
Sudhakar Shinde
2020-10-9
1 个投票
May be position of t(n+1)=t(n)+h; coulb be at the starting of loop.
6 个评论
Lucas Howarth
2020-10-9
Sudhakar Shinde
2020-10-9
Welcome. Glad to help you.
Lucas Howarth
2020-10-9
Sudhakar Shinde
2020-10-9
Is any specific reason to use t(n+0.5)?
I am not sure about mathematical equation but if t(n+0.5) can be replaced with t(n+1), your error will get resolved.
Lucas Howarth
2020-10-9
更多回答（1 个）
J. Alex Lee
2020-10-9
0 个投票
The error is telling you that at the first step of your loop (n=1), you are trying to access the n=2nd element of t and y, but at the stage, t and y are only scalars (arrays with only 1 element) variables. You are trying to access an element of the "arrays" that doesn't exist.
if you are trying to implement implicit Euler, your problem is math, not coding.
2 个评论
J. Alex Lee
2020-10-9
my bad, i didn't look very closely. i guess you are doing a 2 step RK, and it is probably right according to Sudhakar's answer.
Sudhakar Shinde
2020-10-9
yup.
类别
在 帮助中心 和 File Exchange 中查找有关 Mathematics 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by 
